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Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence results and error bounds are obtained for mapped tent pitching schemes made with standard discontinuous Galerkin discretizations for spatial approximation on mapped tents. Techniques to study semidiscretization on mapped tents, design fully discrete schemes, prove local error bounds, prove stability on spacetime fronts, and bound error propagated through unstructured layers are developed.
A spacetime domain can be progressively meshed by tent shaped objects. Numerical methods for solving hyperbolic systems using such tent meshes to advance in time have been proposed previously. Such schemes have the ability to advance in time by diffe
Let $A$ be a real $ntimes n$ matrix and $z,bin mathbb R^n$. The piecewise linear equation system $z-Avert zvert = b$ is called an textit{absolute value equation}. We consider two solvers for this problem, one direct, one semi-iterative, and extend their previously known ranges of convergence.
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the rela
We consider linear systems $Ax = b$ where $A in mathbb{R}^{m times n}$ consists of normalized rows, $|a_i|_{ell^2} = 1$, and where up to $beta m$ entries of $b$ have been corrupted (possibly by arbitrarily large numbers). Haddock, Needell, Rebrova an
Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider solving s